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SAT Math: Systems of Equations (Drill 2)

Drill 2 · Math · Systems of Equations

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About This Drill

SAT Math: Systems of Equations (Drill 2) is a Math practice drill covering Systems of Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT systems of equations questions test substitution, elimination, determining whether a system has one, zero, or infinitely many solutions, and interpreting the solution of a system in a real-world context.

Questions & Explanations

Question 1. x = 3y − 5 and 2x + y = 18. What is the value of y?

  • A) 2
  • B) 3
  • C) 3.5
  • D) 4 ✓

Explanation: Substitute: 2(3y − 5) + y = 18. 6y − 10 + y = 18. 7y = 28. y = 4.

Question 2. A coffee shop sells lattes for $5 and teas for $3. They sold 80 drinks for $310 total. How many lattes were sold?

  • A) 30
  • B) 35 ✓
  • C) 40
  • D) 45

Explanation: L + T = 80 and 5L + 3T = 310. Substitute T = 80 − L: 5L + 240 − 3L = 310. 2L = 70. L = 35.

Question 3. 3x + ky = 9 and 6x + 8y = 15. For what value of k does the system have no solution?

  • A) 2
  • B) 3
  • C) 4 ✓
  • D) 6

Explanation: For no solution (parallel lines), multiply first equation by 2: 6x + 2ky = 18. Need 2k = 8, so k = 4. Then 6x + 8y = 18 vs. 6x + 8y = 15, parallel.

Question 4. x + 2y = 6 and 3x − 2y = 2. What is the value of x + y?

  • A) 4 ✓
  • B) 5
  • C) 6
  • D) 7

Explanation: Add equations: 4x = 8, x = 2. Then 2 + 2y = 6, y = 2. x + y = 4.

Question 5. 3x + 2y = 22 and x − 2y = −6. What is the value of x?

  • A) 3
  • B) 4 ✓
  • C) 5
  • D) 6

Explanation: Add equations: 4x = 16, x = 4. Check: 3(4) + 2y = 22, y = 5. 4 − 10 = −6 ✓.